SOLUTION: Using the Angle-Side-Angle triangle, A=72.4°, C=38.7°, b=3.8cm. What are the values for Angle B, a, and c? A.) 68.9; 3.88cm; 2.72cm B.) 68.9; 3.88cm; 2.55cm C.) 68.9; 2.72cm;

Algebra ->  Test -> SOLUTION: Using the Angle-Side-Angle triangle, A=72.4°, C=38.7°, b=3.8cm. What are the values for Angle B, a, and c? A.) 68.9; 3.88cm; 2.72cm B.) 68.9; 3.88cm; 2.55cm C.) 68.9; 2.72cm;      Log On


   

Question 1068333: Using the Angle-Side-Angle triangle, A=72.4°, C=38.7°, b=3.8cm.
What are the values for Angle B, a, and c?
A.) 68.9; 3.88cm; 2.72cm
B.) 68.9; 3.88cm; 2.55cm
C.) 68.9; 2.72cm; 3.88cm
D.) 68.9; 2.55cm; 3.88cm
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Law of sines
a/sin A=a/sin 72.4=a/0.9532
b/sin B=3.8/sin 68.9(angles sum to 180)=4.0731
c/sin C=c/sin 38.7=c/0.6252
c=0.6252*4.073=2.55
a=3.88
B

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
First of all, angle B = 180° - 72.4° - 38.7° = 68.9°.

Now, apply the Law of sines (see the lesson Law of sines in this site)

b%2Fsin%28B%29 = a%2Fsin%28A%29,

which gives you

3.8%2Fsin%2868.9%5Eo%29 = a%2Fsin%2872.4%5Eo%29.

Find "a" from here: a = %283.8%2Asin%2872.4%5Eo%29%29%2Fsin%2868.9%5EO%29.

Use your calculator.

Similar procedure works for "c".